A368845 Number of solutions to +- 1^3 +- 2^3 +- 3^3 +- ... +- n^3 = n^3.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 4, 0, 0, 8, 187, 0, 0, 831, 1086, 0, 0, 7127, 3983, 0, 0, 20086, 120445, 0, 0, 674006, 1056938, 0, 0, 6983613, 5964500, 0, 0, 40031490, 142694311, 0, 0, 853687222, 1622335105, 0, 0, 10288998770, 12509111104

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2024

Keywords

• nonn

Crossrefs

Cf. A063890, A158118, A348892.

Programs

Maple

b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
      b(abs(n-i^3), i-1) +b(n+i^3, i-1))))((i*(i+1)/2)^2)
    end:
a:= n-> `if`(irem(n, 4)>1, 0, b(n^3, n)):
seq(a(n), n=0..53);  # Alois P. Heinz, Jan 22 2024

Formula

a(n) = [x^(n^3)] Product_{k=1..n} (x^(k^3) + 1/x^(k^3)).